Clematis Montana killed during winter

My 8 year old C.M. which rambled over an arch has been nuked during a rather harsh winter, unusual hot early spring and then two severe frosts.  I have checked the stems and there's not a piece of green so it will all have to be cut down. 

I would like to leave the roots in situ in the hope it will send up new shoots (nothing so far).  Is there any liklihood of this?

I have two Montana Prevail and I though the first one died two winters ago but it came back in the autumn. The following winter both looked like they had died since it was even worse. Cut them back and they came back with a vengance. No flower last year but this loads of them. I would not give up hope yet. The weaker one of mine took almost nine months to recover.

I've had montanas and alpinas wiped out by late, heavy frosts as they are coming into bud and they have not recovered so I don't grow them anymore.  I also have to treat most of my group 2s as group 3s as their top growth usually gets cut back by frost.   Funnily enough, Group 1 Clematis Red Ballon and Red Robin don't have this problem and are going strong even after 4 really bad winters in succession.

For your montana, it's worth cutting back the dead top growth and then waiting to see if the roots have survived and push up new shoots.  This may take few months but will be helped along if you can scatter a generous handful of pelleted chicken manure around the roots and give it a boost of liquid rose or tomato food.

My Montana died back completely this Winter too - all trace of it above ground gone. Had given up on it, 'til I noticed a green shoot poking out of the earth mid-April. We're in London, so possibly warmer than when you are - give it a little time and see - it may surprise you.

It is remarkably hard to kill clematis montana - I'd be inclined to wait a while and see what happens.  My huge pink one was accidentally cut into several bits by my neighbour, who thought each loop over the fence was a separate plant and I would be grateful for the cut back (!!!),  and it ended up with no growth at all, just an 18 inch high 6 inch across stump.   I left it in (not that I could remove it anyway), and this year it has come back with a good helping of new growth.   My neighbour and I are still on speaking terms, he just will ask me if there is anything on our common fence that he wants to cut befiore he does it!

It wasn't as cold as last year but we had a warm spell early on and then a very hard frost.  

If a heavy frost comes soon after the sap has started rising and the plants are juicy and set to burst forth with leaf and flower, it will kill them.  That's what's happend to several of my roses, some other shrubs, my wisteria and a couple of clems too.  Usually, we're still in perma frost till mid March or early April so growth starts late.  This year we had an unusually warm spell in February and things got giddy, to their cost.

Thank you everyone who gave their advice and encouragement.  I will cut it down to the ground and wait.  Fingers crossed.